Observations on the Wilson fermions in the epsilon regime

Abstract

We make several observations concerning the low quark mass region with Wilson fermions and how this is connected with the epsilon regime in the continuum. A transition from tiny cutoff effects to rather large discretization errors would take place in general with Wilson fermions if we lower the quark mass at finite lattice spacing. We argue that these two regions exhibit rather different behaviours concerning the coupling between cutoff effects and zero-modes. We interpolate between these two regimes adding to the continuum epsilon regime formulae, in the spirit of the Symanzik expansion, the relevant operators parametrising the leading cutoff effects. We compute the partition function, the chiral condensate, scalar and pseudo-scalar correlation functions. The final formulae can be used to fit lattice data to extract physical low energy constants, and to estimate systematic uncertainties coming from discretization errors. Moreover they suggest ways on how to remove these cutoff effects, the core of which are captured by the continuum zero modes.

arXiv comment17 pages, 1 figure. v2: few typos corrected. Published on PLB

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• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• The Realization of the Sharpe-Singleton Scenario
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory
• The $\epsilon$-regime of dilaton chiral perturbation theory
• Interpolation between the epsilon and p regimes
• The epsilon regime with twisted mass Wilson fermions
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Chiral Dynamics With Wilson Fermions
• The epsilon regime of chiral perturbation theory with Wilson-type fermions
• Topology, Random Matrix Theory and the spectrum of the Wilson Dirac operator
• Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement
• Exploring the Aoki regime
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• Finite volume corrections to LECs in Wilson and staggered ChPT
• Exploring the epsilon regime with lattice Wilson fermions